Before a monoclonal antibody (or other biological ligand) can label or kill a tumor cell, it must first reach that cell. For portions of a tumor far from the nearest blood vessel or other source of antibody, access may be limited by the rate at which the molecule can "percolate" through the extracellular space. We are investigating the spatial and temporal profiles of immunoglobulin (Ig) distribution generated by diffusion and convection through tumors, taking into account the possibilities of (a) saturable specific binding to cells, (b) nonsaturable, nonspecific binding, and (c) metabolic degradation. We first developed theoretical models of the percolation process, using a VAX 11/780 computer and a program package for numerical solution of partial differential equations. Significant predictions thus far include the following: (1) The diffusion coefficient and/or hydraulic conductivity may limit flux of antitumor Ig through tumors. (2) The flux of non-binding control Ig is much less likely to be limited by diffusion or convection. Nonspeciic Ig's penetrate more deeply and more quickly into the tumor. (3) Even with staturable binding (but not metabolism), the "C times T" exposure of tumor cells to antibody will be the same throughout the mass. (4) Metabolism will decrease the relative "C times T" exposure of cells farther from the source. This may be a major barrier to effective treatment of solid tumors with ligand molecules (or, for that matter, with standard chemotherapeutic agents). We are testing predictions of the model using human melanoma cells injected i.v. in nude mice to form metastatic nodules. The distribution of antibody will be determined by fluorescence techniques and autoradiography. Concepts arising from this study are being applied to the design of clinical studies with monoclonal antibodies. In addition to the investigations of immunoglobulin and other ligands as administered agents, we are considering the physiology of endogenous molecular species including the antibodies, lymphokines, and other growth factors.